Abstract

Statistical process control (SPC) is a method of monitoring, controlling and improving a process through statistical analysis. In real applications, many industrial process data may follow a positively-skewed distribution such as the lognormal distribution. In this article, under lognormal process, we study the performance of three $\overline{X}$ control charts, Shewhart control chart, weighted variance control chart and weighted standard deviation control chart, based on the in-control expected average run length (AARL). The standard deviation of ARL (SDARL) metric is used to evaluate the performance for various amounts of phase I data. A formula to approximate the ARL by the normal approximation method is established in this study. The in-control and out-of-control performance of the three $\overline{X}$ control charts are compared based on the normal approximation and simulation.

摘要

统计过程控制 (SPC) 是一种通过统计分析来监控、控制和改进过程的方法。在实际应用中，许多工业过程数据可能遵循正偏分布，例如对数正态分布。在本文中，在对数正态过程下，我们研究了三个$\overline{X}$控制图、休哈特控制图、加权方差控制图和加权标准偏差控制图，基于在控制的预期平均运行长度 (AARL)。ARL 标准差 (SDARL) 度量标准用于评估不同数量的第一阶段数据的性能。本研究建立了一个用正态逼近法逼近ARL的公式。三者的受控与失控表现$\overline{X}$控制图基于正态近似和模拟进行比较。